Multioperations are operations from a finite set A to set of all subsets of A. The usual composition operator leads to a continuum of closed sets. Therefore, the research of closure operators, which contain composition and other operations becomes necessary. In the paper, the closure of multioperations that can be obtained using the operations of adding dummy variables, identifying variables, composition operator, and operator with the equality predicate branching is studied. We obtain eleven precomplete closed classes of multioperations of rank 2 and prove the completeness criterion. The diagram of inclusions for one of the precomplete class is presented.

Vladimir Panteleev, Dr. Sci. (Phys.–Math.), Prof., Institute of mathematics, economics and informatics, Irkutsk State University, 664000, Irkutsk, K. Marks str., 1, tel.:+7(3952)242214, e-mail: vl.panteleyev@gmail.com

Leonid Riabets, Cand. Sci. (Phys.–Math.), Associate Professor, Institute of mathematics, economics and informatics, Irkutsk State University, 664000, Irkutsk, K. Marks str., 1, tel.:+7(3952)242214, e-mail: l.riabets@gmail.com

Panteleev V.I., Riabets L.V. The completeness criterion for closure operator with the equality predicate branching on the set of multioperations on two-element set. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 29, pp. 68-85. https://doi.org/10.26516/1997-7670.2019.29.68

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